Article
| Title: | On the signless Laplacian and normalized signless Laplacian spreads of graphs (English) |
| Author: | Milovanović, Emina |
| Author: | Bozkurt Altindağ, Serife B. |
| Author: | Matejić, Marjan |
| Author: | Milovanović, Igor |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 2 |
| Year: | 2023 |
| Pages: | 499-511 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $G=(V,E)$, $V=\{v_1,v_2,\ldots ,v_n\}$, be a simple connected graph with $n$ vertices, $m$ edges and a sequence of vertex degrees $d_1\geq d_2\geq \cdots \geq d_n$. Denote by $A$ and $D$ the adjacency matrix and diagonal vertex degree matrix of $G$, respectively. The signless Laplacian of $G$ is defined as $L^+=D+A$ and the normalized signless Laplacian matrix as $\mathcal {L}^+=D^{-1/2}L^+ D^{-1/2}$. The normalized signless Laplacian spreads of a connected nonbipartite graph $G$ are defined as $r(G)= \gamma _{2}^{+}/ \gamma _{n}^{+}$ and $l(G)=\gamma _{2}^{+}-\gamma _{n}^{+}$, where $\gamma _1^+ \ge \gamma _2^+\ge \cdots \ge \gamma _n^+ \ge 0$ are eigenvalues of $\mathcal {L}^+$. We establish sharp lower and upper bounds for the normalized signless Laplacian spreads of connected graphs. In addition, we present a better lower bound on the signless Laplacian spread. (English) |
| Keyword: | Laplacian graph spectra |
| Keyword: | bipartite graph |
| Keyword: | spread of graph |
| MSC: | 05C50 |
| MSC: | 15A18 |
| idZBL: | Zbl 07729520 |
| idMR: | MR4586907 |
| DOI: | 10.21136/CMJ.2023.0005-22 |
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| Date available: | 2023-05-04T17:47:38Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151670 |
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